Ben Miles as Thomas Cromwell, left, and Lydia Leonard as Anne Boleyn in Bring up the Bodies. Photograph: Kirsty Wigglesworth/AP

A small group of American showbiz figures (including Mel Brooks and Whoopi Goldberg) are known as EGOTs because of winning Emmy, Grammy, Oscar and Tony awards. Hilary Mantel, though, may be on course to become the founding member of the TOMB club, as the first author to have written a story that has claimed Man Booker, Olivier, Tony and Bafta awards.

Mantel's literary prizes are already in the bag for the first two parts – Wolf Hall and Bring Up the Bodies – of her projected trilogy about Henry VIII's fixer, Thomas Cromwell. After selling out its RSC premiere at Stratford and breaking West End straight-play box office records for the two-part stage version that opened in London on Saturday, theatre honours will surely follow here and in New York, and anticipation is already building for an unrelated BBC TV version.

The extraordinary enthusiasm for these books across page, stage and screen is partly due to the inherent dramatic power of the narratives: Henry VIII is probably the only figure, apart from Jesus Christ, of whom even the most truanting British schoolchild will have heard.

Even so, Mantel and dramatist Mike Poulton and director Jeremy Herrin bring to the familiar tale of doomed wives and religious convulsion a thrilling originality of psychology and storytelling. Elegantly compressing 1,246 pages of print into just over five and a half hours of stage time, the productions compellingly combine absolute dramatic clarity with tantalising historical ambiguity.

The complex interactions of some 70 characters (seven of them annoyingly called Thomas) are always sharply delineated, but the audience is left to decide whether lurid allegations against Anne Boleyn of adultery and even incest were slander by her murderous husband or held some truth in her desperate attempts to save her life by conceiving an heir.

The attribution of villainy and heroism also challenges conventional biography. Among a uniformly thoughtful and inventive cast, Sir Thomas More (John Ramm), is vain and slippery, a man for all treasons, and yet still ultimately admirable in his willingness to die for principle. Nathaniel Parker's Henry switches instantly between charm, insecurity and terrifying rage, while convincingly suggesting that English ecclesiastical reform was driven by the king's soul as well as his penis. With equal nuance, Paul Jesson's tremendous Cardinal Wolsey is a sybaritic hypocrite but still heart-breaking in his fall, while Lydia Leonard's Anne is a sexual and theological schemer – the plays intriguingly explore the theory that Henry's succession needs gave an opening to Protestant plotters in his court – who later takes on true tragic force.

Crucially, Ben Miles, as Cromwell, is harder on the character than Mantel was. His Master Secretary, on stage almost throughout, is charismatic and attractive, but chilling in moments when he alludes to having killed in Italy or forgets himself and nearly throttles Wolsey and Henry. Cromwell's brutal compliance in letting several people die to save himself was also clearer to me as a theatre-goer than a reader.

Slightly trimmed and rewritten since Stratford, the productions now impress even more with their astonishing narrative economy: the widowing of Cromwell is staged in seconds and, in a startling manipulation of image, what seems to be a funeral becomes a wedding. Seeing the pieces for a second time, I was also more struck by how Mantel and Poulton, while themselves rewriting history, show the king and his spin doctor doing the same. Confronted with "the past" or "the facts", Cromwell calmly avers that these can be changed.

The two great fathers of historical theatre, William Shakespeare and Friedrich Schiller, both touched on the Tudor era – in Henry VIII and Mary Stuart – though with limitations caused by English political fear and German cultural distance respectively. Poulton, an accomplished adapter of Schiller, has created for the Royal Shakespeare Company two fast, darkly comic plays that have clearly learned from those earlier masters but will also not disappoint fans of modern political dramas such as House of Cards.

The Saturday press day meant that, for the first time in 45 years, I missed an FA Cup final on TV, but I have no regrets. Mantel has pledged that she is making haste with the final book in the trilogy, The Mirror and the Light. We must hope that the RSC can reunite as many of this team as possible for an eventual three-play, nine-hour theatrical climax of Mantel's great project.